WEBVTT 00:00:00.000 --> 00:00:05.740 Welcome back to CSE 316 — Data Communication and Networking, and welcome back after the midterm. 00:00:05.790 --> 00:00:12.860 This is the detailed video version of Session fourteen, and it is the bridge session. 00:00:12.910 --> 00:00:20.630 Equal subnetting from Session twelve becomes the full allocation discipline that next week's ISP problem needs. 00:00:20.680 --> 00:00:27.620 There is exactly one new idea: blocks of different sizes can share one parent, if you round up, sort, and align. 00:00:27.670 --> 00:00:36.620 Everything else is drill — and the drill is what makes it worth twelve marks in a fortnight. 00:00:37.325 --> 00:00:40.295 New week, new customer. 00:00:40.345 --> 00:00:45.795 One slash twenty-four — two hundred and fifty-six addresses. And three departments. 00:00:45.845 --> 00:00:51.095 Engineering wants a hundred and twenty. Accounts wants sixty. Reception wants ten. 00:00:51.145 --> 00:00:59.005 Before the midterm you knew exactly one move: equal pieces. So cut quarters — sixty-four each. 00:00:59.055 --> 00:01:05.455 And I claim you have just failed all three departments. Not one. All three, in three different ways. 00:01:05.505 --> 00:01:14.265 Write down what you think those three failures are. One of them is obvious; the other two are the ones equal cutting hides. 00:01:14.315 --> 00:01:23.265 The session is one idea and three rules: a slash twenty-five, a slash twenty-six and a slash twenty-eight can live peacefully inside one slash twenty-four. 00:01:24.735 --> 00:01:33.685 Write a hundred and twenty, sixty and ten in the corner of your page. They stay there all session, and they are answered in the last five minutes. 00:01:36.436 --> 00:01:39.686 Section one. The freedom, and its price. 00:01:39.736 --> 00:01:41.856 Unequal pieces, one parent. 00:01:41.906 --> 00:01:50.856 The freedom is real, and it is not free. The price is three rules, and the whole lecture is those three rules. 00:01:52.027 --> 00:01:58.497 Equal cutting has genuinely run out of moves, rather than merely being inelegant. 00:01:58.547 --> 00:02:04.367 Quarters of sixty-four. A hundred and twenty machines will not go into sixty-four addresses. 00:02:04.417 --> 00:02:09.467 Refused outright, before anything else is even considered. 00:02:09.517 --> 00:02:14.067 Fine — halves of a hundred and twenty-eight, then. Now Engineering fits. 00:02:14.117 --> 00:02:20.297 But you own two pieces and you have three departments. There is nowhere to put the third. 00:02:20.347 --> 00:02:26.267 Equal cutting has exactly one dial: how many pieces. Two, four, eight, sixteen. 00:02:26.317 --> 00:02:32.687 That is the entire range of the tool, and none of the settings solves this. 00:02:32.737 --> 00:02:38.547 So the request list is unequal, and the design has to be allowed to be unequal too. 00:02:38.597 --> 00:02:47.547 Notice that this is a fit problem, not an arithmetic problem. The arithmetic has not changed at all since Session eleven. 00:02:48.970 --> 00:02:52.370 So here is the object we are building today. 00:02:52.420 --> 00:02:59.380 A slash twenty-five, a slash twenty-six and a slash twenty-eight, all inside one slash twenty-four. 00:02:59.430 --> 00:03:06.830 Three blocks of three different sizes, sharing one parent, with no gaps and no overlaps. 00:03:06.880 --> 00:03:15.410 And every piece is still a block. So every piece still obeys the Session eleven ritual: N, mask, first address, last address. 00:03:15.460 --> 00:03:20.080 Nothing you have learned is being replaced. 00:03:20.130 --> 00:03:25.860 And every piece is still a subnet, so "usable" is still N minus two. 00:03:25.910 --> 00:03:31.030 The only new thing is that the pieces are allowed to be different sizes from each other. 00:03:31.080 --> 00:03:40.030 If that feels like a small change, that is the right reaction. One freed constraint — and three rules to keep it legal. 00:03:41.289 --> 00:03:44.069 Rule one. Round up. 00:03:44.119 --> 00:03:53.069 Sizes are powers of two, with no exceptions. So Engineering's hundred and twenty becomes a hundred and twenty-eight — a slash twenty-five, with eight seats spare. 00:03:55.529 --> 00:03:59.289 And that spare is not waste. It is the cost of legality. 00:03:59.339 --> 00:04:07.319 Allocating exactly a hundred and twenty addresses makes the whole design wrong from the first line. 00:04:07.369 --> 00:04:14.129 Accounts: sixty rounds to sixty-four. A slash twenty-six — snug, with four to spare. 00:04:14.179 --> 00:04:19.039 And Reception: ten rounds up to sixteen. A slash twenty-eight. 00:04:19.089 --> 00:04:23.039 Up, always up. Ten machines do not fit in eight addresses. 00:04:23.089 --> 00:04:31.629 Add them: a hundred and twenty-eight, plus sixty-four, plus sixteen, is two hundred and eight of the two hundred and fifty-six demanded. 00:04:31.679 --> 00:04:38.972 So it should fit. Whether it does fit is rules two and three. 00:04:39.022 --> 00:04:45.712 All three rules on one slide, and then we spend the rest of the session on them. 00:04:45.762 --> 00:04:51.872 Rule one: round up. Every request becomes the next power of two, upward, never downward. 00:04:51.922 --> 00:04:59.772 Because no other block size exists — a "block of a hundred and twenty" cannot be written as a prefix at all. 00:04:59.822 --> 00:05:06.032 Rule two: sort descending. Place the largest block first, then the next, and so on. 00:05:06.082 --> 00:05:13.312 Because the largest block has the fewest legal starting positions, so it should choose while it still can. 00:05:13.362 --> 00:05:18.452 Rule three: align. Every block starts on a multiple of its own size. 00:05:18.502 --> 00:05:25.782 That is Session eleven's divisibility rule, promoted to law. A block that fails it is not a block. 00:05:25.832 --> 00:05:30.862 And then audit: allocated plus free equals total. Write the line out. 00:05:30.912 --> 00:05:37.252 It catches your own errors before a grader does, and it is the cheapest mark on the paper. 00:05:37.302 --> 00:05:46.252 That is the whole lecture. Five moves, in that order, and the design falls out — in ninety seconds, with no legal alternative. 00:05:46.312 --> 00:05:55.262 Rule three is the one with teeth. Rules one and two exist mostly to make rule three pass without a fight. 00:05:56.889 --> 00:06:02.619 Now rule three properly, because it is the one that decides everything. 00:06:02.669 --> 00:06:10.169 A one-twenty-eight-block has two legal doors inside a slash twenty-four: offset zero, and offset one twenty-eight. 00:06:10.219 --> 00:06:14.559 There is no third option and no argument to be had. 00:06:14.609 --> 00:06:20.919 A sixty-four-block has four. A thirty-two-block has eight. A sixteen-block has sixteen. 00:06:20.969 --> 00:06:26.089 Multiples of its own size, every time, all the way down. 00:06:26.139 --> 00:06:35.089 So the largest tenant is the fussiest. It has the least freedom, and it is the one most likely to be refused if it arrives late. 00:06:35.709 --> 00:06:44.659 Which is exactly why rule two says largest first: place the fussiest tenant while the building is empty, and every other tenant still finds a door behind it. 00:06:45.419 --> 00:06:53.872 And say this in your head every time you place a block: next FREE is not next LEGAL. 00:06:54.962 --> 00:07:01.272 Forty-two seconds, and the whole argument for why the order is not a matter of taste. 00:07:01.322 --> 00:07:06.472 There are the three requests, and the two failures of equal cutting side by side. 00:07:06.522 --> 00:07:15.472 Quarters refuse Engineering. Halves give you two rooms for three departments. One dial, and neither setting works. 00:07:15.532 --> 00:07:22.962 Round up. A hundred and twenty becomes a hundred and twenty-eight, sixty becomes sixty-four, ten becomes sixteen. 00:07:23.012 --> 00:07:31.702 And underneath: two hundred and eight of two hundred and fifty-six. It should fit — which is a different claim from "it does". 00:07:31.752 --> 00:07:37.252 Rule three, with a legal case and an illegal one. One twenty-eight over sixty-four is two — legal. 00:07:37.302 --> 00:07:46.252 Sixteen over sixty-four is nought point two five — and worse: run that block's own mask over its own first address and the AND says it starts at zero. 00:07:48.482 --> 00:07:54.402 Now the lattice. A slash twenty-five has two doors. A slash twenty-six has four. 00:07:54.452 --> 00:08:01.122 Those tick marks are not decoration — they are every legal starting position that exists. 00:08:01.172 --> 00:08:05.342 Eight for a slash twenty-seven, sixteen for a slash twenty-eight. 00:08:05.392 --> 00:08:13.302 Two, four, eight, sixteen. The bigger the piece, the fewer places it is allowed to stand. 00:08:13.352 --> 00:08:21.122 So the largest goes first, while both of its doors are still open. Then the slash twenty-six, then the slash twenty-eight. 00:08:21.172 --> 00:08:27.642 Sorting descending does not merely avoid trouble. It manufactures the alignment. 00:08:27.692 --> 00:08:31.732 And the five moves, with the audit line underneath. 00:08:31.782 --> 00:08:40.732 Round up, sort, largest first, align, audit. Run them in order and today's design takes ninety seconds. 00:08:41.908 --> 00:08:49.908 Now the mechanism, because "largest first" is easy to remember and easy to forget the reason for. 00:08:49.958 --> 00:08:58.708 A big block placed first lands on offset zero. And zero is a multiple of absolutely everything, so the check passes trivially. 00:08:58.758 --> 00:09:03.598 And it leaves the next start at a multiple of the big block's size. 00:09:03.648 --> 00:09:07.808 Which is automatically a multiple of every smaller power of two. 00:09:07.858 --> 00:09:16.808 A hundred and twenty-eight is a multiple of sixty-four, of thirty-two, of sixteen. So the next tenant, being smaller, finds its door already open. 00:09:19.058 --> 00:09:26.608 So rule three passes for free. That is not a coincidence and it is not luck — it is what sorting descending is FOR. 00:09:26.658 --> 00:09:35.608 And the converse is the whole of section three: place a small block first and the next boundary is at a multiple of the small size, which the big block cannot use. 00:09:40.288 --> 00:09:44.388 Checkpoint one. Stop the video. 00:09:44.438 --> 00:09:52.718 One. Round up these requests and give each prefix: two hundred, thirty-three, five, sixty-five. 00:09:52.768 --> 00:10:01.718 Two. How many legal starting offsets does a slash twenty-seven have inside a slash twenty-four, and what are the first three? 00:10:02.378 --> 00:10:09.248 Three. Why is "allocate exactly the number of addresses requested" wrong, in one sentence? 00:10:09.298 --> 00:10:10.228 Answers. 00:10:10.278 --> 00:10:19.228 One. Two hundred goes to two fifty-six, a slash twenty-four. Thirty-three to sixty-four, a slash twenty-six. Five to eight, a slash twenty-nine. And sixty-five to a hundred and twenty-eight, a slash twenty-five — because sixty-five does not fit in sixty-four. 00:10:23.728 --> 00:10:32.678 Two. A slash twenty-seven is thirty-two addresses, so eight legal offsets — the multiples of thirty-two. The first three are nought, thirty-two and sixty-four. 00:10:40.068 --> 00:10:49.018 Three. Because block sizes are powers of two, so a block of exactly that many addresses cannot be expressed as a prefix, and no mask can find it. 00:10:53.166 --> 00:10:55.636 Section two. The worked design. 00:10:55.686 --> 00:11:01.936 Fourteen dot twenty-four dot seventy-four dot zero, slash twenty-four, largest first. 00:11:01.986 --> 00:11:10.936 This is Forouzan's own Example eighteen point five, in this session's story. The textbook and this design agree number for number. 00:11:14.616 --> 00:11:20.476 Engineering: a hundred and twenty rounds to a hundred and twenty-eight addresses, a slash twenty-five. 00:11:20.526 --> 00:11:25.666 And it goes first, because it is the fussiest tenant in the queue. 00:11:25.716 --> 00:11:31.256 It starts at offset zero. Fourteen dot twenty-four dot seventy-four dot zero. 00:11:31.306 --> 00:11:40.256 And I still say the alignment check out loud, even here: zero divided by a hundred and twenty-eight is zero. Whole. Legal. 00:11:40.756 --> 00:11:48.116 Last address: nought plus a hundred and twenty-eight minus one — dot one twenty-seven. 00:11:48.166 --> 00:11:53.096 Name: fourteen dot twenty-four dot seventy-four dot zero, slash twenty-five. 00:11:53.146 --> 00:11:58.406 That is Session eleven's ritual, unchanged, run for the first of three times. 00:11:58.456 --> 00:12:06.536 The arithmetic here is unchanged; only the fitting problem around it is new. 00:12:07.546 --> 00:12:12.356 Accounts starts where Engineering stopped: offset one twenty-eight. 00:12:12.406 --> 00:12:21.356 Check: one twenty-eight divided by sixty-four is two. Whole, legal. Name: dot one twenty-eight slash twenty-six, last address dot one ninety-one. 00:12:23.156 --> 00:12:27.446 Reception starts where Accounts stopped: offset one ninety-two. 00:12:27.496 --> 00:12:36.446 Check: one ninety-two divided by sixteen is twelve. Whole, legal. Name: dot one ninety-two slash twenty-eight, last address dot two zero seven. 00:12:39.296 --> 00:12:45.536 And the block did not run out. Dot two zero eight through dot two fifty-five sit unused. 00:12:45.586 --> 00:12:52.256 Forty-eight addresses the organisation keeps for the future — contiguous, and at the end. 00:12:52.306 --> 00:13:01.256 Now audit it like a professional. Every start is a multiple of its own size: nought, one twenty-eight, one ninety-two — divisible by a hundred and twenty-eight, sixty-four and sixteen. 00:13:06.046 --> 00:13:11.926 And the last piece is flush: the design ends exactly where the block does. No gap, no overlap. 00:13:11.976 --> 00:13:20.926 Three tenants, flush against each other, every boundary on a line the arithmetic allows. That is what a full-marks answer looks like. 00:13:25.613 --> 00:13:33.433 A hundred and twenty-eight, plus sixty-four, plus sixteen, plus forty-eight, is two hundred and fifty-six. 00:13:33.483 --> 00:13:40.853 Write it out. Every time, on every design question, as the last line of the answer. 00:13:40.903 --> 00:13:49.853 It catches your own errors before the grader does. A design that fails the sum has a gap, an overlap, or a piece of the wrong size — 00:13:50.153 --> 00:13:55.223 and you will find out in ten seconds rather than in a returned script. 00:13:55.273 --> 00:14:03.213 And it is the cheapest mark on the paper. One line of addition, and the examiner can see that you know what a complete design is. 00:14:03.263 --> 00:14:12.213 If the sum fails, the design is lying to you somewhere. Do not argue with it — go back and find the piece in the wrong place. 00:14:15.707 --> 00:14:22.357 Forty-two seconds, one tenant at a time, with the alignment check on every start. 00:14:22.407 --> 00:14:28.067 An empty bar, two hundred and fifty-six addresses wide, and three requests above it. 00:14:28.117 --> 00:14:34.457 Nothing has been placed. This is what you have at the start of a twelve-mark question. 00:14:34.507 --> 00:14:40.477 Rounded, and the spare seats named on each card: twenty-eight spare, four spare, six spare. 00:14:40.527 --> 00:14:45.387 And the sum: two hundred and eight of two hundred and fifty-six. 00:14:45.437 --> 00:14:54.117 Engineering takes the front door, and watch the check on the block itself: zero divided by a hundred and twenty-eight is zero. Whole, legal. 00:14:54.167 --> 00:14:57.147 Half the bar, in one move. 00:14:57.197 --> 00:15:02.187 Accounts starts where Engineering stopped. One twenty-eight over sixty-four is two. 00:15:02.237 --> 00:15:08.617 Largest-first did not avoid an illegal placement. It manufactured a legal one. 00:15:08.667 --> 00:15:13.577 Reception at one ninety-two. One ninety-two over sixteen is twelve. 00:15:13.627 --> 00:15:20.797 Three tenants, flush against each other, and every boundary on a line the arithmetic allows. 00:15:20.847 --> 00:15:28.717 And the tail: dot two zero eight through dot two fifty-five. Forty-eight addresses, contiguous, at the end. 00:15:28.767 --> 00:15:35.757 It has no prefix yet — it is just a range, and it becomes blocks the day somebody asks. 00:15:35.807 --> 00:15:39.907 And the audit line. Allocated plus free equals total. 00:15:39.957 --> 00:15:47.275 That is the last line of the answer, and it is the cheapest mark on the paper. 00:15:47.325 --> 00:15:54.565 A correct design can still lose marks by being incomplete, so here is exactly what to write down. 00:15:54.615 --> 00:16:01.955 A table with five columns: department, requested, rounded, name with prefix, and last address. 00:16:02.005 --> 00:16:07.525 Anything less is an incomplete answer, however right the numbers are. 00:16:07.575 --> 00:16:16.525 An alignment check beside every start. "One twenty-eight over sixty-four is two" costs you four characters and earns method marks. 00:16:17.505 --> 00:16:24.295 A named leftover: "dot two zero eight to dot two fifty-five unused, forty-eight addresses". 00:16:24.345 --> 00:16:31.645 Say it explicitly. A design that silently ignores the tail looks like a design that lost count. 00:16:31.695 --> 00:16:36.025 And the audit line underneath. One line, and the answer is closed. 00:16:36.075 --> 00:16:45.025 Draw the bar as well if you have time. A to-scale picture takes thirty seconds and makes an overlap visible instantly. 00:16:47.422 --> 00:16:56.372 The leftover is a range, not a block. Dot two zero eight to dot two fifty-five is forty-eight addresses, and forty-eight is not a power of two. 00:16:57.562 --> 00:17:01.442 So it cannot be written as a single prefix. 00:17:01.492 --> 00:17:10.442 It becomes blocks when someone asks. Cut it as needed: a slash twenty-eight at dot two zero eight, a slash twenty-seven at dot two twenty-four. 00:17:11.172 --> 00:17:18.852 And those are legal, because two zero eight divides by sixteen and two twenty-four divides by thirty-two. 00:17:18.902 --> 00:17:24.292 So the organisation has kept its options — which is the practical point of largest-first. 00:17:24.342 --> 00:17:32.579 The unspent addresses end up together, at the end, and still usable. 00:17:32.629 --> 00:17:35.999 Checkpoint two. Stop the video. 00:17:36.049 --> 00:17:43.829 One. In the worked design, why is dot one ninety-two a legal start for a slash twenty-eight? 00:17:43.879 --> 00:17:52.829 Two. Give two legal blocks that together use the forty-eight-address tail from dot two zero eight to dot two fifty-five. 00:17:52.909 --> 00:18:01.859 Three. Write the audit line for a slash twenty-four allocated as sixty-four plus thirty-two plus thirty-two plus sixteen, and say whether it closes. 00:18:03.539 --> 00:18:04.469 Answers. 00:18:04.519 --> 00:18:13.469 One. Because one ninety-two divided by sixteen is twelve — whole. Every start must be a multiple of its own block's size, and one ninety-two is. 00:18:14.919 --> 00:18:23.869 Two. A slash twenty-eight at dot two zero eight, since two zero eight over sixteen is thirteen. And a slash twenty-seven at dot two twenty-four, since two twenty-four over thirty-two is seven. Sixteen plus thirty-two is forty-eight. 00:18:31.229 --> 00:18:40.179 Three. Sixty-four plus thirty-two plus thirty-two plus sixteen is a hundred and forty-four allocated, so a hundred and twelve free — and a hundred and forty-four plus a hundred and twelve is two hundred and fifty-six. It closes, provided every start is aligned. 00:18:51.018 --> 00:18:54.068 Section three. Order is not tidiness. 00:18:54.118 --> 00:19:01.778 Everything so far worked on the first try, and that can breed a dangerous thought: that sorting is merely neat. 00:19:01.828 --> 00:19:10.778 So let us allocate the same three customers smallest first, and watch the arithmetic push back. 00:19:12.376 --> 00:19:19.346 Reception first. Sixteen addresses at offset zero. Zero over sixteen is zero, legal. 00:19:19.396 --> 00:19:24.056 So far nothing has gone wrong — which is exactly the problem. 00:19:24.106 --> 00:19:29.156 Accounts next. The next free address is offset sixteen, so try it. 00:19:29.206 --> 00:19:36.896 Sixteen divided by sixty-four is nought point two five. Not whole. The placement is refused. 00:19:36.946 --> 00:19:45.866 And writing it anyway would be wrong. "Fourteen dot twenty-four dot seventy-four dot sixteen slash twenty-six" is not merely untidy. It is a lie. 00:19:45.916 --> 00:19:52.666 Run its own mask over its own first address and the AND says the block starts at zero — on top of Reception. 00:19:52.716 --> 00:19:57.236 A block that fails its own ritual is not a block. 00:19:57.286 --> 00:20:06.236 That is the sharpest way to state rule three, and it is the sentence worth writing in your notes. 00:20:08.065 --> 00:20:13.305 The only legal door is offset sixty-four. Sixty-four over sixty-four is one, whole. 00:20:13.355 --> 00:20:20.015 So Accounts goes there: dot sixty-four slash twenty-six, running dot sixty-four to dot one twenty-seven. 00:20:20.065 --> 00:20:26.145 And addresses sixteen through sixty-three drop dead. Forty-eight of them. 00:20:26.195 --> 00:20:32.655 Not at the end where they could be sold — in the middle, where they cannot. 00:20:32.705 --> 00:20:40.735 Engineering then takes offset one twenty-eight. One twenty-eight over a hundred and twenty-eight is one, legal. It still fits. 00:20:40.785 --> 00:20:48.805 This time. With six customers and a tighter block, it will not — and that is next session. 00:20:48.855 --> 00:20:56.795 And the warning: the audit still passes. Sixteen plus forty-eight plus sixty-four plus one twenty-eight is two hundred and fifty-six. 00:20:56.845 --> 00:21:03.725 A design can audit correctly and still be bad. The sum checks completeness, not quality. 00:21:03.775 --> 00:21:10.975 Same customers, same total, worse outcome. Largest-first left a future slash twenty-six ready to sell. 00:21:11.025 --> 00:21:19.018 Smallest-first left the same forty-eight addresses trapped between two tenants. 00:21:20.028 --> 00:21:26.478 Both orders, side by side, on the same two hundred and fifty-six addresses. 00:21:26.528 --> 00:21:35.478 Two empty bars, and the three rounded requests above them. The only difference between the top and the bottom is the order. 00:21:35.658 --> 00:21:44.608 Top bar, largest first. Engineering at offset zero, and the check written inside the block: zero over a hundred and twenty-eight is zero. 00:21:45.628 --> 00:21:54.578 Accounts at one twenty-eight. One twenty-eight over sixty-four is two — and notice the door was already open because of what went before it. 00:21:54.758 --> 00:22:03.608 Reception at one ninety-two, and the free tail in grey at the end. Forty-eight addresses, contiguous, with no prefix yet. 00:22:03.658 --> 00:22:09.858 That is the finished design, and the audit line underneath closes at two fifty-six. 00:22:09.908 --> 00:22:17.418 Now the bottom bar. Reception first, at offset zero. Perfectly legal, and completely wrong. 00:22:17.468 --> 00:22:24.318 And there is the refusal, in red: sixteen over sixty-four is nought point two five. Not whole. 00:22:24.368 --> 00:22:31.218 Read the second half of that panel — the reason the name would be false, not merely untidy. 00:22:31.268 --> 00:22:39.578 Skip to sixty-four, and forty-eight addresses are stranded — drawn in red, in the middle of the block, between two tenants. 00:22:39.628 --> 00:22:48.578 Same total, same audit, and a design a professional would redo. Open it and step through both orders yourself. 00:22:51.008 --> 00:22:54.268 The same forty-eight addresses, in a different place. 00:22:54.318 --> 00:23:03.268 At the end of the block they are a contiguous range you can cut into legal blocks the day a customer appears. Between two tenants they are forty-eight addresses nobody can grow into. 00:23:06.348 --> 00:23:12.468 And the organisation cannot rearrange. Once Reception has an address, it has an address. 00:23:12.518 --> 00:23:17.418 Moving a live subnet means renumbering every machine on it. 00:23:17.468 --> 00:23:21.868 And next session, wrong order does not scar. It overflows. 00:23:21.918 --> 00:23:30.868 Six organisations, in two waves, and nobody in wave one may move when wave two lands. A customer who cannot be placed at all is a different kind of failure. 00:23:35.706 --> 00:23:39.176 Checkpoint three. Stop the video. 00:23:39.226 --> 00:23:48.176 One. A slash twenty-four is allocated smallest-first: a slash twenty-eight, then a slash twenty-seven, then a slash twenty-five. Where does each land, and what is stranded? 00:23:52.976 --> 00:24:01.676 Two. Why can fourteen dot twenty-four dot seventy-four dot sixteen never name a slash twenty-six, whatever the designer intended? 00:24:01.726 --> 00:24:10.026 Three. A design audits correctly but wastes forty-eight addresses in the middle. Is it wrong? One sentence. 00:24:10.076 --> 00:24:11.006 Answers. 00:24:11.056 --> 00:24:20.006 One. The slash twenty-eight at dot zero, sixteen addresses. The slash twenty-seven must start on a multiple of thirty-two, so dot thirty-two — stranding sixteen to thirty-one. The slash twenty-five must start on a multiple of a hundred and twenty-eight, so dot one twenty-eight — stranding sixty-four to one twenty-seven. Eighty addresses stranded in total. 00:24:27.766 --> 00:24:36.716 Two. Because sixteen over sixty-four is not whole. Run the slash twenty-six mask over that address and the AND returns dot zero, so the block it belongs to starts at dot zero. The name is simply false. 00:24:46.796 --> 00:24:55.746 Three. It is not incorrect, but it is poor: the audit proves the design is complete, not that the leftovers are usable. Marks for correctness — and a professional would redo it. 00:25:03.082 --> 00:25:06.912 Section four. Drill it until the audit is reflex. 00:25:06.962 --> 00:25:09.072 Two designs, and four ticks. 00:25:09.122 --> 00:25:18.072 The method is five moves long. What makes it worth marks under time pressure is that you can run it without deciding anything. 00:25:20.285 --> 00:25:29.105 One nine two dot one six eight dot seven dot zero, slash twenty-four. Requests: a hundred and twenty, twenty-five, and six. 00:25:29.155 --> 00:25:38.105 Round up all three before you place anything, and write the rounded sizes in a column, largest at the top. That column is your placement order. 00:25:40.555 --> 00:25:48.835 Then place, checking each start against its own size. Offset divided by size, and it must come out whole. 00:25:48.885 --> 00:25:56.855 Stop the video. Three minutes. Four answers: three names with prefixes, and the free range at the end. 00:25:56.905 --> 00:26:04.415 And finish with the audit line: allocated plus free equals two fifty-six, or the design is not finished. 00:26:04.465 --> 00:26:13.415 Three minutes is generous once the five moves are automatic. If it took longer, the thing to drill is the rounding, not the placement. 00:26:17.035 --> 00:26:25.985 Rounded: a hundred and twenty goes to a hundred and twenty-eight, a slash twenty-five. Twenty-five goes to thirty-two, a slash twenty-seven. Six goes to eight, a slash twenty-nine. 00:26:28.975 --> 00:26:37.925 Note the two traps: twenty-five rounds to thirty-two, not sixteen. And six rounds to eight, not four. Upward, always. 00:26:39.635 --> 00:26:47.905 A: one nine two dot one six eight dot seven dot zero, slash twenty-five. Last address dot one twenty-seven. 00:26:47.955 --> 00:26:54.195 Check: zero over a hundred and twenty-eight is zero. Whole, legal. 00:26:54.245 --> 00:26:59.845 B: dot one twenty-eight, slash twenty-seven. Last address dot one fifty-nine. 00:26:59.895 --> 00:27:08.845 Check: one twenty-eight over thirty-two is four. Whole — and it is legal only because the slash twenty-five ate exactly a hundred and twenty-eight first. 00:27:11.825 --> 00:27:17.425 C: dot one sixty, slash twenty-nine. Last address dot one sixty-seven. 00:27:17.475 --> 00:27:22.555 Check: one sixty over eight is twenty. Whole, legal. 00:27:22.605 --> 00:27:28.475 And free: dot one sixty-eight through dot two fifty-five. Eighty-eight addresses. 00:27:28.525 --> 00:27:37.475 The audit: a hundred and twenty-eight, plus thirty-two, plus eight, plus eighty-eight — two hundred and fifty-six. Tick. 00:27:38.015 --> 00:27:46.965 Look at B again. Largest-first did not merely avoid waste; it manufactured the alignment that made B legal in the first place. 00:27:49.612 --> 00:27:57.482 One seventy-two dot sixteen dot four dot zero, slash twenty-three. Requests: two hundred, a hundred and twenty, sixty. 00:27:57.532 --> 00:28:06.482 Five hundred and twelve addresses this time, so the design will step over the dot four, dot five boundary in the third octet. Do not let that frighten you. 00:28:08.922 --> 00:28:14.702 Stop the video. Three minutes. Round up, sort, place, align, audit. 00:28:14.752 --> 00:28:21.482 Same five moves; the only difference is that the offsets are bigger than two fifty-six. 00:28:21.532 --> 00:28:30.482 And think in offsets, not in dots. The starts are at offsets nought, two fifty-six and three eighty-four — divisible by two fifty-six, a hundred and twenty-eight and sixty-four. 00:28:33.772 --> 00:28:36.712 The dots are just how the offsets get written down. 00:28:36.762 --> 00:28:45.712 This is your homework block from last session. If you did the four-way equal cut, you already know where one seventy-two dot sixteen dot five dot zero sits. 00:28:50.602 --> 00:28:59.552 Rounded: two hundred goes to two hundred and fifty-six, a slash twenty-four. A hundred and twenty goes to a hundred and twenty-eight, a slash twenty-five. Sixty goes to sixty-four, a slash twenty-six. 00:29:05.732 --> 00:29:14.682 Note that two hundred rounds all the way to a full slash twenty-four — there is no size between a hundred and twenty-eight and two fifty-six. 00:29:16.722 --> 00:29:25.672 A: one seventy-two dot sixteen dot four dot zero, slash twenty-four. Last address one seventy-two dot sixteen dot four dot two fifty-five. 00:29:25.732 --> 00:29:31.332 Check: offset zero over two fifty-six is zero. Whole, legal. 00:29:31.382 --> 00:29:40.062 B: one seventy-two dot sixteen dot five dot zero, slash twenty-five. Last address dot five dot one twenty-seven. 00:29:40.112 --> 00:29:47.332 Check: offset two fifty-six over a hundred and twenty-eight is two. Whole, legal. 00:29:47.382 --> 00:29:55.862 C: one seventy-two dot sixteen dot five dot one twenty-eight, slash twenty-six. Last address dot five dot one ninety-one. 00:29:55.912 --> 00:30:02.302 Check: offset three eighty-four over sixty-four is six. Whole, legal. 00:30:02.352 --> 00:30:09.552 And free: dot five dot one ninety-two through dot five dot two fifty-five. Sixty-four addresses. 00:30:09.602 --> 00:30:17.502 The audit: two fifty-six plus a hundred and twenty-eight plus sixty-four plus sixty-four — five hundred and twelve. Tick. 00:30:17.552 --> 00:30:26.502 The octet boundary changes nothing: the slash twenty-four ends at dot four dot two fifty-five and the slash twenty-five starts at dot five dot zero. 00:30:31.091 --> 00:30:39.061 The five moves, live, with the audit line computed for you — and the tool refuses everything illegal. 00:30:39.111 --> 00:30:47.551 It opens with the requests and nothing placed. The five move-cards along the top are all grey, and the bar is empty. 00:30:47.601 --> 00:30:55.451 Move one lights up: a hundred becomes a hundred and twenty-eight, sixty becomes sixty-four, ten becomes sixteen. 00:30:55.501 --> 00:31:04.251 And the note underneath names the spare seats — thirty-eight in total, and it calls them the cost of legality rather than waste. 00:31:04.301 --> 00:31:10.491 Move two. Sorted descending, and that column is now the placement order. 00:31:10.541 --> 00:31:18.461 Engineering placed, and look at the last column of the table: zero divided by a hundred and twenty-eight equals zero, tick. 00:31:18.511 --> 00:31:22.881 The alignment check is a column, not an afterthought. 00:31:22.931 --> 00:31:27.491 Accounts at one twenty-eight, with its own check beside it. 00:31:27.541 --> 00:31:36.491 Reception at one ninety-two, and the free row appears in grey — forty-eight addresses, "no prefix yet", and the note that it becomes blocks when someone asks. 00:31:38.181 --> 00:31:46.731 And the audit line closes: a hundred and twenty-eight plus sixty-four plus sixteen plus forty-eight is two fifty-six. 00:31:46.781 --> 00:31:55.731 And the drill preset, so you can check your own answer: dot zero slash twenty-five, dot one twenty-eight slash twenty-seven, dot one sixty slash twenty-nine, and eighty-eight free. 00:31:59.091 --> 00:32:08.041 Try the overflow preset too — a hundred and thirty, sixty and thirty on a slash twenty-four. Watch the audit turn red and tell you no ordering can fix it. 00:32:12.597 --> 00:32:21.547 Copy this board into your notes verbatim. Four ticks, and you run all four before an examiner ever sees the answer. 00:32:21.707 --> 00:32:26.307 Tick one: powers of two? Every allocated size is two to the n. 00:32:26.357 --> 00:32:34.007 A request of a hundred allocated as a hundred fails here immediately, before anything else is checked. 00:32:34.057 --> 00:32:37.057 Tick two: sorted? Largest placed first. 00:32:37.107 --> 00:32:42.927 If not, expect stranded addresses even when the sum still closes. 00:32:42.977 --> 00:32:47.857 Tick three: aligned? Every start divided by its own size is whole. 00:32:47.907 --> 00:32:55.607 This is the one an examiner checks first, and the one the hardware enforces whether or not anyone checks it. 00:32:55.657 --> 00:33:01.437 And the fourth tick: allocated plus free equals total. Four ticks, full marks. 00:33:01.487 --> 00:33:10.430 Any cross — redesign, because a design that fails one tick usually fails silently everywhere else. 00:33:11.440 --> 00:33:16.750 Next session, an ISP is granted eleven dot ten dot three dot ten, slash twenty-two. 00:33:16.800 --> 00:33:24.890 That is the same block you have been carrying since Session eleven. A thousand and twenty-four addresses. 00:33:24.940 --> 00:33:32.220 Six organisations arrive, in two waves. And nobody in wave one may move when wave two lands — 00:33:32.270 --> 00:33:36.640 because renumbering a live network is not an option. 00:33:36.690 --> 00:33:43.980 So the ordering stops being a preference. With six customers and a fixed parent, wrong order does not scar. 00:33:44.030 --> 00:33:48.720 It overflows — a customer who cannot be placed at all. 00:33:48.770 --> 00:33:57.140 Bring this session's ritual. Round up, sort, largest first, align, audit — six times, with a seating plan. 00:33:57.190 --> 00:34:06.140 Everything you need for twelve marks is in this session and Session eleven. What is added next week is only the scale, and the two-wave constraint. 00:34:09.356 --> 00:34:15.806 Checkpoint four, and this is the rehearsal for next week. Stop the video. 00:34:15.856 --> 00:34:24.806 One. Design two hundred dot one dot one dot zero slash twenty-four for requests of sixty, sixty and a hundred. Give names, prefixes and the free range. 00:34:30.056 --> 00:34:39.006 Two. Requests of a hundred and thirty, sixty and thirty arrive for a single slash twenty-four. What happens, and what do you tell the customer? 00:34:44.176 --> 00:34:47.716 Three. State the four audit ticks from memory. 00:34:47.766 --> 00:34:48.616 Answers. 00:34:48.666 --> 00:34:57.616 One. Rounded: a hundred and twenty-eight, sixty-four, sixty-four — and sorted, the hundred goes first. Two hundred dot one dot one dot zero slash twenty-five, then dot one twenty-eight slash twenty-six, then dot one ninety-two slash twenty-six. No free range. Audit: a hundred and twenty-eight plus sixty-four plus sixty-four is two fifty-six. Tick. 00:35:07.306 --> 00:35:16.256 Two. A hundred and thirty rounds to two fifty-six, sixty to sixty-four, thirty to thirty-two — a total of three hundred and fifty-two, which is more than two hundred and fifty-six. It overflows, and no ordering can fix it. The customer needs a slash twenty-three. 00:35:21.246 --> 00:35:30.196 Three. Powers of two. Sorted descending. Every start divisible by its own size. Allocated plus free equals total. 00:35:37.611 --> 00:35:41.291 Five ways to lose marks on a design question. 00:35:41.341 --> 00:35:46.791 Wrong: Engineering asked for a hundred, so allocate a hundred addresses. 00:35:46.841 --> 00:35:55.791 Right: a hundred and twenty-eight. Sizes are powers of two, so a block of exactly a hundred cannot be written as a prefix at all. 00:35:56.801 --> 00:36:02.481 Wrong: Reception needs ten, so give it a slash twenty-nine — eight addresses. 00:36:02.531 --> 00:36:11.481 Right: round up. A slash twenty-eight, sixteen addresses. Ten machines do not fit in eight — and "usable" makes it worse, because a slash twenty-nine seats six. 00:36:14.441 --> 00:36:18.431 Wrong: place them in the order the customer listed them. 00:36:18.481 --> 00:36:26.301 Right: sort descending first. Customer order is arbitrary; placement order is arithmetic. 00:36:26.351 --> 00:36:32.461 Wrong: the next free address is dot sixteen, so the slash twenty-six starts at dot sixteen. 00:36:32.511 --> 00:36:41.461 Right: next legal, not next free. Sixteen over sixty-four is not whole, so the next legal door is dot sixty-four. 00:36:41.821 --> 00:36:46.941 And wrong: the design is finished when every department has a block. 00:36:46.991 --> 00:36:55.941 Right: it is finished when the audit line closes — allocated plus free equals total, written out. 00:36:56.078 --> 00:37:01.148 Back to minute one. Why did equal quarters fail all three? 00:37:01.198 --> 00:37:10.148 Engineering: too small. Sixty-four addresses for a hundred machines. Refused outright, and the most obvious of the three. 00:37:11.918 --> 00:37:20.868 Accounts: lucky. Sixty fits inside sixty-four with four to spare — but only by accident, and one new hire breaks it. 00:37:21.058 --> 00:37:23.088 Luck is not a design. 00:37:23.138 --> 00:37:27.048 And Reception: wasteful. Fifty-four of its sixty-four addresses idle forever. 00:37:27.098 --> 00:37:32.988 Not a failure you notice on day one, and exactly the kind an ISP charges you for. 00:37:33.038 --> 00:37:41.988 Too small, too lucky, too wasteful. Three departments, three different failures, one cause: the cut ignored the requests. 00:37:46.040 --> 00:37:54.990 Round every request up to a power of two, on sight — and say why exact allocation is illegal rather than merely untidy. 00:37:55.740 --> 00:38:04.690 Sort descending and place largest first — and explain that sorting is what makes the alignment pass, not merely what makes it neat. 00:38:05.320 --> 00:38:13.660 Check every start against its own size. Offset over size, whole or refused, with no appeal. 00:38:13.710 --> 00:38:22.660 And close every design with the audit line: allocated plus free equals total, written out, every time. 00:38:25.063 --> 00:38:30.073 The fifty, fifty, one hundred redesign — with a proof about the ordering. 00:38:30.123 --> 00:38:38.903 The lesson there is subtle: request order might survive. You must demonstrate whether it does, not decide by feel. 00:38:38.953 --> 00:38:47.903 Example eighteen point five, re-run cold. No notes. Five moves, ninety seconds, and the audit line at the bottom. 00:38:48.773 --> 00:38:53.873 And keep eleven dot ten dot zero dot zero slash twenty-two in front of you. 00:38:53.923 --> 00:39:01.903 One line, six customers, two waves, twelve marks. It arrives next session and it does not wait. 00:39:01.953 --> 00:39:10.903 Reading: Forouzan eighteen point four on block allocation, plus the IP block allocation problem sheet, parts a to c. 00:39:14.169 --> 00:39:20.669 One: round up. Every request to the next power of two, upward only. 00:39:20.719 --> 00:39:28.519 Two: sort descending. The placement order is arithmetic, not the customer's email. 00:39:28.569 --> 00:39:37.519 Three and four: place largest first, and align each start. Offset over its own size, whole — or find the next legal door. 00:39:38.599 --> 00:39:43.689 Five: audit. Allocated plus free equals total, written as a line of the answer. 00:39:43.739 --> 00:39:51.842 Five moves, in that order, and a design that has no legal alternative. 00:39:51.892 --> 00:39:53.702 That is Session fourteen. 00:39:53.752 --> 00:39:58.302 Round up, sort, largest first, align — then audit. 00:39:58.352 --> 00:40:04.982 Blocks of different sizes share one parent, provided every start is a multiple of its own size. 00:40:05.032 --> 00:40:13.982 And order is not tidiness. Sorting descending is the thing that makes the alignment pass, and getting it wrong strands addresses in the middle of your block. 00:40:14.302 --> 00:40:21.382 If the sum check fails, the design is lying to you somewhere. Find the piece, do not argue with the arithmetic. 00:40:21.432 --> 00:40:30.382 Before the next session: the fifty-fifty-hundred redesign with a proof about ordering, Example eighteen point five re-run cold, and eleven dot ten dot zero dot zero slash twenty-two in your notes. 00:40:33.652 --> 00:40:39.282 Next: one line, six customers, two waves — and nobody in wave one may move. 00:40:39.332 --> 00:40:44.292 I will see you there.